Estimating and correcting for contrast agent extravasation in tissue perfusion imaging

ABSTRACT

The invention provides a method, an image analysis software product, and a system for medical imaging analysis for estimating contrast agent extravasation in contrast agent based perfusion imaging such as MRI dynamic contrast enhanced (DCE) imaging, and in particular correction, compensation, or visualization of extravascular leakage of contrast agent in tumors. According to the invention, the effect of extravasation is directly manifested in the tail part of an observed, apparent residue function, R′(t), obtained directly by de-convoluting the expression C(t)=R′(t) C p ′(t) with the arterial input function (AIF). A leakage rate or extravasation constant is determined directly from the tail part of the determined apparent residue function. The invention also relates to distinguishing between T 1 -dominant and T 2 *-dominant extravasation effects in perfusion imaging to from the sign of the tail part of the determined apparent residue function and to an automated method for DSC-MRI involving correction for contrast agent extravasation and partial volume effects.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a non-provisional of and claims the benefit of priority to U.S. provisional Patent Application Ser. No. 61/325,019, filed on Apr. 16, 2010, the disclosures of which are hereby expressly incorporated by reference in their entireties.

FIELD OF THE INVENTION

The present invention relates to perfusion analysis based on dynamic contrast enhanced (DCE) imaging, in particular correction or compensation due to extravascular leakage of the contrast agent in tumors.

BACKGROUND OF THE INVENTION

In DCE imaging, an MRI or CT sequence is recorded after a contrast agent (CA) has been injected intravenously. The recorded sequence consist of dynamic concentration time curves (CTC) recorded for each voxel, which shows the contrast agent induced signal (˜which can be related to relative CA concentration) in a given voxel as a function of time. Thereby, DCE imaging can be used to make a quantitative estimates of tissue perfusion and tissue blood volume, i.e. the amount of blood per unit tissue volume and per unit time that flow through the capillaries of the vascular bed of a given tissue region. These quantitative estimates of tissue perfusion metric can reveal details related the type and state of the tissue, also referred to herein as hemodynamic parameters. In particular, dynamic susceptibility contrast (DSC) MRI is an increasingly used method to characterize brain tumors and in particular gliomas. Several studies have shown that DSC-MRI can be used to improve tumor grading and further to predict patient prognosis and treatment response.

However, a number of artefacts appear in DCE imaging, two of which are the subject of the present invention.

An important step in quantitative tumor perfusion analysis is related to correction for extravascular leakage of the contrast agent into the tumor tissue. Many brain tumors result in disrupted blood-brain-barrier (BBB) causing the contrast agent to leave the intravascular space and leak into the interstitial space. This extravasation has a confounding effect on the estimations of tumor blood volume and perfusion unless corrected for

One particular mathematical correction method has become widely used is described in Boxerman et al., American Journal of Neuroradiology 27 (2006), 859-67 as well as in U.S. Pat. No. 6,807,441. The method suggested herein corrects for extravasation by assuming relaxation to be dominated by T₁-shortening and then correct for leakage relative to an average first-pass pass response for the entire image slice. The method implicitly assumes that the variation in tissue MTT and delay is small relative to the slice average MTT/delay. Given the highly heterogeneous vasculature in tumor such as gliomas, MTT/delay values which deviate significantly from the mean MTT are very likely and may lead to incorrect estimations of contrast agent extravasation. This method is used as a reference method and is denoted Method I in the following.

Another method described in U.S. Pat. No. 7,567,832 and Quarles et al., Magnetic Resonance in Medicine 53 (2005), 1307-1316. A disadvantage of this approach is that a very long time series is needed to correctly identify the leakage term from the apparent residue function and further that CBV leakage correction cannot be performed directly from the residue function.

Hence, improved ways of estimating and correcting for extravascular leakage of contrast agent would be advantageous.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an improved procedure for estimating extravasation rates and/or correcting extravascular leakage of contrast agent in contrast agent based perfusion imaging such as DCE MRI and CT imaging.

It is another object of the present invention to provide a method for estimating contrast agent extravasation in contrast agent based perfusion imaging such as MRI dynamic contrast enhanced (DCE) imaging that solves the above mentioned problems of the prior art with correction of extravascular leakage of the contrast agent.

It is a further object to provide a method, a computer program and a system for correction of contrast agent extravasation.

Further objects relate to a method of distinguishing between T₁-dominant and T₂*-dominant extravasation effects in perfusion imaging and an automated method for DSC-MRI involving correction for contrast agent extravasation and partial volume effects.

In the prior art, it is customary to represent the measured contrast agent concentration, C(t), in the absence of extravasation as a result of a convolution between the concentration time curve in an artery feeding the tissue of interest, C_(p)(t) (the arterial input function, AIF) and a residue function; R(t) so that C(t)=F·R(t)

C_(p)(t), where R(t) describes the fraction of injected contrast agent still present in a tissue voxel at time t and F is tissue perfusion. In the mathematical analysis used to estimate perfusion, the perfusion scaled residue function R_(ps)(t)=FR(t) can be estimated and perfusion is then given by the value of R_(ps)(t) at t=0.

To take leakage into consideration, two different methods have been proposed in the prior art. In Method I (U.S. Pat. No. 6,807,441 and Boxerman et al), extravasation is estimated by comparing the tissue response curve averaged for all brain voxels without leakage (identified by certain a priori assumptions about the shape of C(t) in the absence of leakage) with the tissue response in any given voxel. Any deviation in the shape of C(t) for a given voxel relative to the mean C(t) is then assumed to be due to extravasation. From this, the relative extravasation rate constant can then be estimated by applying an appropriate kinetic model. This method implicitly assumes that any deviation in shape of C(t) is only due to extravasation effects. However, variations in tissue transit times or delay times may also result in deviations in the shape of C(t) relative to the mean curve, and this would then be misinterpreted as extravasation.

In a modified correction method (U.S. Pat. No. 7,567,832 and Quarles et al.), the leakage constant is estimated from the tissue residue function directly by making certain (strict) assumptions about the properties of the leakage effect. The estimated leakage constant is then back-substituted into the expression used in Method I to obtain corrected CBV values. The advantage of this method is that the resulting leakage constant is not affected by deviations in tissue transit times. The disadvantage of this method is that the resulting estimation of the leakage constant is very sensitive to the underlying mathematical methods used to derive the residue function and will only give correct estimates for very long time series. Further, the method must be combined with method I to obtain corrected CBV values.

C_(p)(t) may e.g. be estimated from the signal in voxels only containing plasma such as large arteries. It is noted, that estimation of C_(p)(t) (or AIF) is an entire field in itself, and that several techniques for this are well known to the skilled person, see e.g. Mouridsen et al., Automatic Selection of Arterial Input Function Using Cluster Analysis, Magnetic Resonance in Medicine 55:524-531 (2006). The leakage correction procedure present invention involves the advantage that it is not critically dependent on which technique is applied for estimating C_(p)(t).

In the present invention, the extravasation constant is also estimated directly from the residue function which makes the method insensitive to variations in mean transit times. However, different from the prior art, the leakage constant is estimated directly from curve fitting of the resulting in an observed, leakage-affected residue function, referred to as the apparent residue function R′(t), without including the leakage term as an explicit parameter in the mathematical model used to derive R(t). This has the advantage of making the estimation of R′(t) more robust with less restrictions on the underlying kinetic model and also, after the leakage constant is estimated from R′(t), a leakage corrected residue function can be estimated and from this leakage corrected CBV can be determined directly without the need to re-generate tissue response curves.

It is thus assumed that that the effect of extravasation can be directly accounted for in the apparent residue function and that extravasation correction of the acquired signal is therefore not necessary prior to deconvolution with the estimated C′_(p)(t). The apparent residue function R′(t), like the ideal residue function R(t), has an initial peak or maximum followed by a decaying “tail”, which is a result of the contrast agent kinetics can be separated into two distinct hemodynamic phases. The present invention is based upon the realisation that the effect of extravasation is directly manifested in the tail part of the observed residue function which would be expected to have a zero asymptote in the absence of extravasation. The initial portion of the apparent residue function describes the intravascular effect of the contrast agent during the capillary passage whereas the later phase of the apparent residue function reflects the degree of extravasation of the agent from the intravascular space (IVS) to the extravascular extracellular space (EES) (and the reflux from EES to IVS). According to the invention, a first leakage rate constant K_(a) (also referred to as K′ in previous version of this application) quantifying an apparent rate of contrast agent extravasation from plasma (IVS) to extravascular, extracellular space (EES) is estimated directly from a tail part of the apparent residue function.

Typically, the signal is recorded during consecutive passages of the contrast agent through the vascular system, until the signal becomes very weak. In order to contain data representing the tail part of the apparent residue function, the signal should at least be recorded from before the first passage and until significant extravasation has occurred.

The invention proposes an alternative methodology for correction of contrast agent extravasation effects. According hereto, a leakage rate constant K_(a) can be estimated directly from the deconvolution procedure. This provides the advantage of giving a more correct estimate of the mean transit time (MTT) in the presence of extravasation and also a more correct estimate of cerebral blood volume (CBV) in regions with altered MTT and/or contrast agent delay combined with significant extravasation effects. Further, the inventors have previously shown that CBV can be accurately determined directly from the tissue residue function in non-leaky tissue (see Bjornerud et al., A fully automated method for quantitative cerebral hemodynamic analysis using DSC-MRI. J Cereb Blood Flow Metab 30:1066-1078.), and by direct extravasation correction of the residue function according to an embodiment of the invention, the same method can be used to estimated leakage corrected CBV.

Thus, in a first aspect, the invention provides a method for estimating contrast agent extravasation in contrast agent based perfusion imaging in accordance with claim 1.

In a second aspect, the invention provides a method of distinguishing between T₁-dominant and T₂*-dominant extravasation effects in perfusion imaging to from the sign of the tail part of the determined apparent residue function and producing maps or images visualizing the dominant extravasation effect. The method comprises the following steps to be performed by an electronic processor:

-   -   accessing perfusion image data comprising a signal related to         contrast agent concentration as a function of time in a voxel         during the first and consecutive passages of the contrast agent         through the vascular system;     -   representing the signal by a convolution, R_(ps)′(t)         C_(p)′(t), of an apparent residue function, R_(ps)′(t), and an         estimated contrast agent concentration in plasma, C_(p)′(t), and         determining the apparent residue function R_(ps)′(t) by         deconvolution of the signal with C_(p)′;     -   determining a sign of the tail part of the apparent residue         function; and     -   generating an image of a parameter reflecting at least the         determined sign and preferably also a magnitude of the tail         part.

In a third aspect, the invention provides an automated method for DSC-MRI involving correction for contrast agent extravasation and partial volume.

In a fourth aspect, the invention provides a method for producing an image of contrast agent extravasation corrected hemodynamic parameter values with a medical imaging system.

In a fifth aspect, the invention provides an image analysis software for contrast agent based perfusion images, the image analysis software comprising a module for estimating contrast agent extravasation in contrast agent based perfusion image data.

In a sixth aspect, the invention provides a system for medical imaging analysis.

In the following description of the invention, a number of embodiments and preferred and/or optional features, elements, examples and implementations will be described. Features or elements described in relation to one embodiment, implementation or aspect may be combined with or applied to the other embodiments, implementations or aspects where applicable. For example, features applied in relation to a method may also be used as features in relation to software or a system and vice versa. Also, explanations of underlying mechanisms of the invention as realized by the inventors are presented for explanatory purposes, and should not be used in ex post facto analysis for deducing the invention.

K_(a) is similar to, but not identical to K^(trans). K^(trans) quantifies the rate of contrast agent extravasation from plasma to extravascular, extracellular space (EES) when calculated in absolute quantitative terms (in units of mL/100 g/min). As will be described later, contrast agent extravasation artefacts results from a combination of both T₁ and T₂* effects so that a signal change cannot be directly related to CA concentration. K_(a) therefore quantifies an apparent rate of contrast agent extravasation, and can substitute K^(trans) in equations and algorithms for hemodynamic parameters.

The tissue residue function is the fraction of contrast agent concentration at time t (for the case of an ideal instantaneous bolus injected at t=0). However, since a large number of distortions and other effects are present, this strictly theoretical definition is mainly used in mathematical modelling. When performing practical calculations on real data, several other residue functions are relied upon. In the present description, the following terminology is used:

-   R(t) Tissue residue function, the fraction of contrast agent     concentration at time t for the case of an ideal instantaneous bolus     injected at t=0. -   R_(ps)(t) Perfusion scaled residue function, R_(ps)(t)=FR(t), where     F=tissue perfusion or flow. This is the parameter that is commonly     estimated by mathematical deconvolution of C(t) with C_(p)(t), and     the tissue response and perfusion is then given by the amplitude of     R_(ps)(t) at t=0 (or the peak amplitude with t>0 in case of delay     effects). In previous version of this application, no explicit     difference between whether the residue function was perfusion scaled     or not was made. -   R_(ps)′(t) Perfusion scaled apparent residue function, the observed     tissue residue function scaled by tissue flow and influenced by     contrast agent extravasation and other distortions. This is what is     determined from deconvolution of the measured C(t) with C_(p)′(t)     (AIF) in accordance with the invention. Is also referred to by R′(t)     in cases where flow/perfusion scaling is implicit. -   R′(t) Apparent tissue residue function, the tissue residue function     influenced by contrast agent extravasation and other distortions;     determined by R′(t)=R_(ps)′(t)/F. As the perfusion scaling is often     implied, the term apparent residue function and the notation R′(t)     are used to refer to both R′(t) and R_(ps)′(t) in the present     description unless explicit distinction is made. -   R_(corr)(t) Leakage corrected tissue residue function, determined     from R′(t) or R_(ps)′(t) and K_(a).

In embodiments of the various aspects, it is preferred that an extravasation corrected residue function, R_(corr)(t), is determined from the apparent residue function R′(t) and the estimated K_(a). Then, using the first leakage rate constant K_(a) or the extravasation corrected residue function R_(corr)(t), extravasation corrected hemodynamic parameters may preferably be estimated for each voxel, such as one or more of: an extravasation-corrected CBV value, an extravasation-corrected mean transit time (MTT), and an extravasation-corrected bolus delay (T_(max)). Such extravasation-corrected CBV value will reflect the true intravascular volume and is unaffected by contrast agent extravasation.

Additionally, the proposed method allows for correction of both T₁- and T₂*-dominant leakage effects. Here, T₁-dominant leakage effect refers to the situation where the CA results in a signal increase (T₁-shortening) after extravasation whereas T₂*-dominant leakage refers to the situation where the CA results in a signal reduction (T₂- or T₂* shortening) after extravasation. Both effects can occur in brain tumors following extravasation depending on many factors both related to the underlying tumor microstructure as well as properties of the MR sequence used to generate the DSC-MRI data. It may therefore be preferred that K_(a) is allowed to take both positive and negative values, and that the invention further comprises separating between T₁- and T₂*-dominant leakage by determining the sign of K_(a), so that negative K_(a) values reflect T₁-dominant leakage effects and positive K_(a) values reflect T₂*-dominant leakage effects. In a preferred embodiment, this distinguishing between T₁-dominant and T₂*-dominant extravasation effects is utilized to produce maps or images visualizing the dominant extravasation effect by imaging of e.g. the sign of the tail part of the apparent residue function (Sign|R′(t>>T_(c))|), K_(a), the sign of K_(a), or similar.

In preferred embodiments, the imaged tissue is (preferably automatically) segmented into a tumor region and white and/or grey matter, and a mean value of K_(a) are estimated for the tumor region.

The various aspects of the invention may be used to obtain quantitative assessment of multiple hemodynamic parameters in tumors, such as tumor classification, detection of malignant transformations; monitoring of therapy response, estimation of survival, and longitudinal monitoring.

In the present description, the signal related to contrast agent concentration as a function of time in voxels may be a change in amplitude of a contrast agent induced signal as recorded by a medical imaging apparatus such as an MR or CT scanner, or any signal derived there from. The intensity change is to be interpreted broadly and may e.g. be in the form of a relaxation rate or relative contrast agent concentration. Preferably, the signal is a concentration time curve (CTC). In one embodiment, the medical imaging apparatus is preferably an MR apparatus and the perfusion image data is recorded in a T₂ or T₂* weighed sequence. Alternatively or additionally, the perfusion data may include T₁ weighed sequence.

References to tumors are to be understood as a general reference to the following types: intra-axial brain tumors (e.g. gliomas), mammary tumors, prostate tumors, head and neck tumors, and intracranial metastasis, unless explicitly specified that the context in question. However, in preferred embodiments, the various aspects of the inventions are limited to intra-axial brain tumors, such as intra-axial primary brain tumors, preferably gliomas.

Embodiments of the various aspects of the invention relates to image analysis software, typically implemented as a computer program product. Such computer program product is adapted to enable a computer system comprising at least one computer having data storage means associated therewith to carry out the invention. Such a computer program product may be provided on any kind of computer readable medium, e.g. magnetically or optically based medium, or through a computer based network, e.g. the Internet.

The basic idea of the invention is to estimate extravasation rates or constants to be used in correcting for extravascular leakage by a new approximation of a tail part of an apparent tissue residue function accounting for the loss of contrast agent from the intravascular space (corresponding to the leakage of contrast agent into tissue).

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a flow diagram embodying the methods for correcting perfusion image data and the software applications according to various aspects of the invention.

FIG. 2 illustrates a medical image analysis system 20 for implementing different embodiments for the various aspects of the invention.

FIGS. 3A and B illustrate the determination of K_(a) and optionally k_(ep) from the apparent residue function R′(t).

FIG. 4 shows a series of images from a clinical sample case of a grade 2 glioma with strong T₂* dominant leakage as well as a graph showing the corresponding apparent residue functions from normal white matter and tumor.

FIGS. 5A and B are graphs showing AIFs from multiple slice in a single subject corrected for PVEs. FIG. 5A shows AIFs automatically detected in each slice and FIG. 5B shows the corresponding average AIF across all slices together with the average venous output function (VOF). Gamma variate fitted curves are used to determine the steady-state portion and the PV correction factor is determined from the difference in the steady state levels of the AIF and VOF, respectively.

FIGS. 6A-C show the results of the simulation of the correlation between K_(a) and K^(trans) as function of flip angle (6A), extra-vascular transverse relaxivity (r2_(ev)) (6B) and presence or absence of pre-dose (6C).

FIGS. 7A and B show the correlations between the estimated CBV and MTT after extravasation correction using the two correction methods compared to actual- and uncorrected values.

FIGS. 8A and B show the simulated error in K₂ (ΔK₂) as a function of nMTT (8A) and the corresponding error in rCBV (ΔrCBV) in percent after correction using Method I (8B) in the situation of no CA extravasation (E=0).

FIG. 9A shows two glioblastoma cases demonstrating T₁-dominant (left) and T₂*-dominant extravasation effects. FIG. 9B shows the corresponding dose-response curves and residue functions for the same two sample cases.

FIG. 10 shows two selected sample cases (upper/lower row) demonstrating the effect of elevated tumor MTT values.

FIGS. 11A-C show pixel-wise analysis of error in K₂ and rCBV as function of nMTT for two clinical cases selected based on the presence of a large range of nMTT values in tumor.

FIG. 12 shows Kaplan-Meier survival curves.

DETAILED DESCRIPTION OF AN EMBODIMENT

The generalized flow diagram of FIG. 1 embodies the methods for correcting perfusion image data according to the various aspects of the invention. FIG. 1 further embodies the layout of software applications according to the various aspects of the invention.

The invention can be implemented by means of hardware, software, firmware or any combination of these. The invention or some of the features thereof can also be implemented as software running on one or more data processors and/or digital signal processors.

FIG. 2 illustrates a medical image analysis system 20 for implementing different embodiments for the various aspects of the invention.

The system 20 has means 21 for receiving or accessing image data to be processed or already processed (i.e. post-processed) image data from an image recording apparatus such as a CT or MR scanner and/or internal or external storage 24 holding images recorded by such apparatus such as a PACS. The means 21 may e.g. be a data bus allowing access to a memory, an internet connection, or a cable or wireless connection. The system comprises a computer 25 or a similar processing apparatus holding an electronic processor 26 and memory 27 for holding and executing software or computer programs relating to the image analysis modules according to embodiments of the invention using the received image data. The system can further comprise user interface 29 (e.g. keyboard, mouse, touch screen etc.) for receiving user input. The determined corrections factors or corrected data or parameters can be presented to the user via a display 28 and/or stored in the storage 24.

As suggested, the storage may include access to a Picture Archival and Communication System (PACS). This is a system for storage of images and transferring images between computers in different facilities through networks. This system consists of devices to produce and store digital images electronically, workstations to view and interpret images, and a network linking computers from different sites. Appropriate PACS software allows the interpreter to manipulate images as needed, at his own location, by retrieving images from other locations via PACS. The PACS connects different computers through a high-speed network to share information. This connection can be in a single department using a local area network (LAN), in a hospital using the intranet, or outside the hospital via the Internet.

The individual elements of an embodiment of the invention may be physically, functionally and logically implemented in any suitable way such as in a single unit, in a plurality of units or as part of separate functional units. The invention may be implemented in a single unit, or be both physically and functionally distributed between different units and processors.

Correction for Extravascular Leakage

The estimating of contrast agent extravasation in contrast agent based perfusion imaging is described in the following with reference to the flow diagram 10 of FIG. 1.

INV: I have incorporated your new box, forgot tracked changes . . . . Dynamic perfusion imaging data reflecting MR signal intensity variations S(t) due to contrast agent administration is accessed (box 1), and pixel-wise converted to contrast agent concentration in tissue, C(t), as a function of time in voxels during the first and consecutive passages of the contrast agent through the vascular system, box 2.

In box 3, an estimated contrast agent concentration in plasma, C_(p)′(t), such as preferably an AIF is determined, preferably automatically e.g. using the clustering method suggested in Bjornerud et al. However, other estimations of the contrast agent concentration may also be used. The signal is then represented by a convolution, R_(ps)′(t)

C_(p)′(t), of an apparent residue function, R_(ps)′(t), and the (perfusion scaled) apparent residue function R_(ps)′(t) can be determined by deconvolution of the signal with the estimated C_(p)′(t), box 4.

In box 5, a first leakage rate constant K_(a) quantifying an apparent rate of contrast agent extravasation from plasma to extravascular, extracellular space (EES) can be estimated based on a tail part of the apparent residue function R_(ps)′(t) (or R′(t)).

Depending of the approach, it might be required to determine where, i.e. at which time, the tail part starts. For this purpose, the tail part of the apparent residue function can be determined in many different ways, such as by one or more of:

-   -   fitting a singly peaked, monotonously decreasing function, L(t),         with zero asymptotes to a global maxima peak of the apparent         residue function and defining the tail part of the apparent         residue function as the part where the amplitude of the apparent         residue function is consistently larger than the amplitude of         L(t);     -   estimating the approximate mean transit time from the perfusion         image data and from this estimate a time, t_(tp), larger than         MTT and using R_(ps)′(t) for t>t_(tp) as the tail part of the         apparent residue function;     -   finding the section of the apparent residue function following         its peak amplitude with minimum relative variance (variance         divided by mean value) over a predefined section length; e.g.         equal to a given fraction of the total number of data points         from the peak to the last data point of the apparent residue         function.     -   Fitting the apparent residue function to a composite of multiple         functions describing the different portions of the residue         function.

However, in other approaches involving fitting of functions to the apparent residue function, it may not be necessary to separately identify the tail part as the shape of the fitted function and the fitting procedure automatically extracts K_(a) from the right part of R_(ps)′(t).

Some preferred approaches for estimating K_(a) is given here:

-   -   K_(a) is estimated as being proportional to a mean value of the         tail part of the apparent residue function.     -   K_(a) is estimated as being proportional to an asymptote of the         apparent residue function.     -   the estimation comprises fitting an exponential or linear         function involving K_(a) as a constant to at least the tail part         of the apparent residue function.

It is noted that numerous other ways of determining Ka from the tail part of R_(ps)′(t) can be made. Also, as extravasation is mainly an issue in pathologic tissue, it is generally not of specific interest to determine R′(t), K_(a), etc. for e.g. normal grey and white matter. It is therefore also possible to first perform a tissue segmentation and only make the determinations according to the invention in potentially pathologic tissue.

Optionally, as indicated in box 6, a second leakage rate constant k_(ep) quantifying an apparent rate of contrast agent reflux from tissue back to blood (from EES back to IVS) can also be estimated based on the tail part of the apparent residue function. K_(a) and k_(ep) are preferably determined for each voxel in the image data.

When K_(a) and optionally k_(ep) have been determined, an extravasation corrected residue function, R_(corr)(t), is preferably determined from the apparent residue function R_(ps)′(t) and the estimated K_(a), this is box 7.

The extravasation corrected residue function, R_(corr)(t), is preferably determined using at least one of the following algorithms: R _(corr)(t)=R′(t)−K _(a) R _(corr)(t)=1/F(R _(ps)′(t)−K _(a)(1−k _(ep) t)) R _(corr)(t)=1/F(R _(ps)′(t)−K _(α) e ^(−k) ^(ep) ^(t)) R _(corr)(t)=1/F(R _(ps)′(t)−mean[R _(ps)′(t>t _(tp))]) where the residue function R′(t) is scaled by a tissue flow, F, and wherein t_(tp) is the estimated start time of the tail part as described above or a capillary transit time of the CA, T_(c), described elsewhere.

Then (box 8), extravasation corrected hemodynamic parameters can be estimated using the first leakage rate constant K_(a) or the extravasation corrected residue function R_(corr)(t), preferably for each voxel. Typical parameters of interest are an extravasation-corrected CBV value, an extravasation-corrected mean transit time (MTT), and an extravasation-corrected bolus delay (T_(max)). An extravasation-corrected CBV value will reflect the true intravascular volume and is unaffected by contrast agent extravasation. In preferred embodiments, maps or images of the extravasation corrected hemodynamic parameters can be produced.

As mentioned previously, the sign of the tail part of the apparent residue function can be used to directly distinguish between T₁-dominant and T₂*-dominant extravasation effects. Thereby, different maps or images can be generated for visualizing the dominant extravasation effect, based on a parameter related to the sign of the tail part of the apparent residue function, such as Sign|R′(t>>T_(c))|, K_(a), Sign|K_(a)|, or similar.

Determined extravasation corrected values, functions, and parameters can be stored and/or presented to a user (box 9).

In more detail, a total contrast agent concentration in a voxel, C_(t) _(—) _(m), is related to the measured signal change induced by the contrast agent, which may be estimated as: C _(t) _(—) _(m) =C _(t) _(—) _(ev) +C _(t) _(—) _(iv), wherein C_(t) _(—) _(iv) is the contrast agent concentration in tissue confined to the intravascular space in the absence of contrast agent extravasation as determined by a one-compartment model:

C_(t_(lr))(t) = F∫₀^(t)R(t − τ)C_(p)(τ)𝕕τ. And wherein C_(t) _(—) _(ev) is the contrast agent concentration in tissue confined to the extravascular space in the presence of contrast agent extravasation as determined by a two-compartment model:

C_(t_(m))(t) = K_(a)∫₀^(t)𝕖^(−k_(ep)(t − τ))C_(p)(τ) 𝕕τ + C_(t_(iv))(t).

Thereby, C_(t) _(—) _(m) can be expressed as

C_(t_(m))(t) = ∫₀^(t)[K_(a)𝕖^((−k_(ep)(t − τ))) + F ⋅ R(t − τ)]C_(p)(τ)𝕕τ where k_(ep) is the rate constant from the EES to the intravascular space, C_(p)(τ) is the contrast agent concentration in plasma, R(t) is an effective tissue specific residue function, and F is proportional to tissue flow. C_(t) _(—) _(m) can be expressed in standard matrix notation as: c=A(r+e)=A(r′), where A is a convolution matrix for a contrast agent concentration in plasma, r is an effective tissue specific residue function, e is an error term due to constant agent extravasation involving K_(a), and r′ is the apparent′ residue function and is given by:

$r^{\prime} = {{r + e} = {\begin{bmatrix} {R\left( t_{0} \right)} \\ {R\left( t_{1} \right)} \\ \vdots \\ {R\left( t_{N - 1} \right)} \end{bmatrix} + {{\frac{K_{a}}{F}\begin{bmatrix} {\mathbb{e}}^{{- k_{ep}}t_{0}} \\ {\mathbb{e}}^{{- k_{ep}}t_{1}} \\ \vdots \\ {\mathbb{e}}^{{- k_{ep}}t_{N - 1}} \end{bmatrix}}.}}}$

As mentioned above, r′ can be determined by deconvolution of the signal by an estimated contrast agent concentration in plasma, preferably the arterial input function.

The present invention involves observing that the residue function contains an exponential “tail” in the presence of extravasation. The error term describing the error in CBV due to extravasation is then given by:

K_(a)∫𝕖^(−k_(ep)t)𝕕t.

Leakage rate constants K_(a) and k_(ep) can thereby be estimated directly from an apparent residue function obtained by deconvolution of the concentration signal, simply based on the tail of the apparent residue function. Several ways of performing this estimation is suggested herein.

In a preferred embodiment the non-leaky part of the apparent residue function (i.e. r or the peak corresponding to the duration of the first pass of contrast agent) can be approximated by a singly peaked function with zero asymptotes, e.g. a Lorenzian. Similarly, the error term (i.e. e or the tail corresponding to times following the first passage can be approximated by a function of K_(a), e.g. a linear expression such as K_(a) t or K_(a) (1−k_(ep)t). Thereby, K_(a) and optionally k_(ep) can be determined by fitting these to the apparent residue function.

One approach to a more detailed derivation of the theory behind the present invention is provided in the following. This approach applies the assumption that the CA leaks into capillary tissue and EES simultaneously, which is a relatively good approach. Later in this description, another, alternative approach which instead assumes that CA extravasation occurs into first into capillary tissue and then, With a time lag, into EES will be presented. There are indications that this last approach better reflects the real situation, and although there is a large overlap in the two approaches, both are fully presented for completeness.

The approach to leakage correction applied by the present invention attempts to account for differences in MTT and delay and incorporate the correction directly into the convolution integral used to estimate tissue perfusion. In the absence of CA extravasation, tissue flow can be estimated by solving the convolution integral:

$\begin{matrix} {{C_{t_{iv}}(t)} = {F{\int_{0}^{t}{{R\left( {t - \tau} \right)}{C_{p}(\tau)}\ {\mathbb{d}\tau}}}}} & (1) \end{matrix}$ Where C_(p) is the tracer concentration in plasma and C_(t) _(—) _(iv), is the tracer concentration in tissue (confined to the intravascular space), R is the tissue specific residue function and F is proportional to tissue flow. Given that C_(t) and C_(p) can be determined, perfusion (in units of mL/100 g/min) can then be estimated from the initial height of the residue function (in the absence of tracer delay) and is given by:

$\begin{matrix} {{CBF} = {\frac{H_{c}}{\rho}F}} & (2) \end{matrix}$ where H_(c) is a factor correcting for the difference in hematocrit in large vessels and capillaries and ρ is tissue density. The mean transit time (MTT) is given by the area under the residue function and from the central volume principle blood volume (CBV) can then be estimated directly from the residue function according to:

$\begin{matrix} {{CBV} = {{{CBF} \cdot {MTT}} = {\frac{H_{c}}{\rho}F{\int_{0}^{t}{{R(t)}\ {\mathbb{d}t}}}}}} & (3) \end{matrix}$

In the situation where the tracer is not confined to the intravascular space, the tracer flux and reflux between the intravascular (i.v.) and extravascular-extracellular space (EES) can be described by a two compartment model as follows:

$\begin{matrix} {{C_{t_{m}}(t)} = {{K^{trans}{\int_{0}^{t}{{\mathbb{e}}^{- k_{{ep}{({t - \tau})}}}{C_{p}(\tau)}\ {\mathbb{d}\tau}}}} + {C_{t_{iv}}(t)}}} & (4) \end{matrix}$ where K^(trans) is the transfer constant from the i.v. space to the EES and k_(ep) is the rate constant from the EES to the i.v. space, C_(p) is the plasma concentration of tracer and C_(t) _(—) _(ev) is the tracer concentration in the extravascular space of tissue, C_(t) _(—) _(iv) is the intravascular tracer concentration.

Combining Eq. 1 and 4 and denoting C_(t) _(—) _(m)=C_(t) _(—) _(ev)+C_(t) _(—) _(iv) as the total tracer concentration in a voxel, we then obtain a single expression incorporating both CA dispersion and extravasation:

$\begin{matrix} {{C_{t_{m}}(t)} = {\int_{0}^{t}{\left\lbrack {K^{{transe}{({- {k_{ep}{({t - \tau})}}})}} + {F \cdot {R\left( {t - \tau} \right)}}} \right\rbrack{C_{p}(\tau)}{\mathbb{d}\tau}}}} & (5) \end{matrix}$

In DSC-MRI, relative CA concentration can only be estimated through measurements of change in the transverse relaxation rate ΔR2*. As discussed below, the apparent ΔR2* may be contaminated by T1-effects during CA extravasation and can therefore not be assumed to reflect CA concentration in the respective tissue compartments. Denoting the apparent rate constant estimated through measurements of ΔR2* in blood and tissue by K′ and accounting for the discrete sampling interval Δt, Eq 5 can be written in matrix notation as:

$\begin{matrix} {\begin{bmatrix} {\Delta\; R\; 2_{t}^{\prime}\left( t_{0} \right)} \\ {\Delta\; R\; 2_{t}^{\prime}\left( t_{1} \right)} \\ \vdots \\ {\Delta\; R\; 2_{t}^{\prime}\left( t_{N - 1} \right)} \end{bmatrix} = {\Delta\;{t \cdot \begin{bmatrix} {\Delta\; R\; 2_{p}^{\prime}\left( t_{0} \right)} & 0 & \ldots & 0 \\ {\Delta\; R\; 2_{p}^{\prime}\left( t_{1} \right)} & {\Delta\; R\; 2_{p}^{\prime}\left( t_{0} \right)} & \ldots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ {\Delta\; R\; 2_{p}^{\prime}\left( t_{N - 1} \right)} & {\Delta\; R\; 2_{p}^{\prime}\left( t_{N - 1} \right)} & \ldots & {\Delta\; R\; 2_{p}^{\prime}\left( t_{N - 1} \right)} \end{bmatrix}} \times \left\{ {{F \cdot \begin{bmatrix} {R\left( t_{0} \right)} \\ {R\left( t_{1} \right)} \\ \vdots \\ {R\left( t_{N - 1} \right)} \end{bmatrix}} + {K_{a} \cdot \begin{bmatrix} {\mathbb{e}}^{{- k_{ep}}t_{0}} \\ {\mathbb{e}}^{{- k_{ep}}t_{1}} \\ \vdots \\ {\mathbb{e}}^{{- k_{ep}}t_{N - 1}} \end{bmatrix}}} \right\}}} & (6) \end{matrix}$

-   -   In the case of contrast agent extravasations, we can thus         substitute the ‘non-leaky’ residue function (r) with an         ‘apparent’ residue function, r′, given by:

$\begin{matrix} {r^{\prime} = {{r + e} = {\begin{bmatrix} {R\left( t_{0} \right)} \\ {R\left( t_{1} \right)} \\ \vdots \\ {R\left( t_{N - 1} \right)} \end{bmatrix} + {\frac{K_{a}}{F}\begin{bmatrix} {\mathbb{e}}^{{- k_{ep}}t_{0}} \\ {\mathbb{e}}^{{- k_{ep}}t_{1}} \\ \vdots \\ {\mathbb{e}}^{{- k_{ep}}t_{N - 1}} \end{bmatrix}}}}} & (7) \end{matrix}$

Eq. 6 can then be written in simplified form as: c=A(r+e)=Ar′  (8)

Now, for the situation where k_(ep)t_(N-1)<<1, the rate constant K_(a) can be incorporated as the final element in the first residue term of Eq. 7 to give a single residue vector:

$\begin{matrix} {r^{\prime} = \begin{bmatrix} {R\left( t_{0} \right)} \\ {R\left( t_{1} \right)} \\ \vdots \\ {R\left( t_{N - 1} \right)} \\ K_{a} \end{bmatrix}} & (9) \end{matrix}$

Equation 8 can then be solved for r′ using standard deconvolution methods like singular value decomposition (SVD).

In a preferred embodiment, K_(a) and optionally also k_(ep) can be estimated directly from the apparent residue function r′, i.e. without the need for solving the equation system of Eq. 9. If k_(ep)t_(N-1)<<1, r′ approaches a value of K_(a) (rather than zero for no leakage). By ensuring that the total dynamic scan time is significantly longer than the tracer transit time in all tissues, K_(a) can then simply be estimated from the offset value of r′ for t>>MTT. If both K_(a) and k_(ep) are significant then the apparent residue function exhibits an exponential ‘tail’ given by K_(a) exp(−k_(ep)t) and the can then be estimated by fitting an exponential or a straight line to the tail of r′.

In another preferred embodiment, k_(ep)t_(N) is assumed to negligible and K_(a) can be estimated using either Eq 9 or by determining the mean offset level of the apparent residue function r′.

The determination of K_(a) and optionally k_(ep) from the apparent residue function is illustrated in the following referring to FIGS. 3A and B. Herein, the apparent residue function, R′(t), in the presence of T₂*- or T₁-dominant extravasation (broken line curves in FIG. 3A or 3B, respectively) are shown relative to an ideal residue function, R(t), with no extravasation (solid line curve 30).

FIG. 3A shows the apparent residue function in the presence of T₂*-dominant extravasation. The dotted curve 31 represents the apparent residue function in the presence of both extravascular leakage (K_(a)>0) and backflux of contrast agent from tissue to blood (k_(ep)>0) whereas the dash-dot curve 32 represents the apparent residue function when k_(ep) is negligible so that k_(ep)t is approx zero for all time points. As seen, the apparent tissue perfusion is over-estimated by a factor K_(a) in the presence of extravasation. In accordance with the invention, K_(a) can be estimated (thin lines 35) from either the constant tail of the residue function (when k_(ep)t˜0, curve 32) or from the intercept of a linear fit of the tail of the apparent residue function when k_(ep)t>0, curve 31).

FIG. 3B shows the apparent residue function in the presence of T₁-dominant extravasation. The dashed curve 33 represents the apparent residue function in the presence of both extravascular leakage (K_(a)<0) and backflux of contrast agent from tissue to blood (k_(ep)>0) whereas the dash-dot curve 34 represents the apparent residue function when k_(ep) is negligible so that k_(ep)t is approximately zero for all time points. As seen, the apparent tissue perfusion is in this case under-estimated by a factor K_(a) in the presence of extravasation. In accordance with the invention, K_(a) can be estimated (thin lines 35) from either the constant tail of the residue function (when k_(ep)t˜0, curve 34) or from the intercept of a linear fit of the tail of the apparent residue function when k_(ep)t>0, curve 33).

When K_(a) and optionally k_(ep) have been determined, image data corrected to take into account extravasation of contrast agent can be calculated and stored and/or presented to a user. Alternatively or additionally, hemodynamic parameter can be calculated using the corrected image data and stored and/or presented to a user. In another alternative, a K_(a) leakage map can be calculated and stored and/or presented to a user.

As an example, the leakage corrected CBV can be given by: CBV_(corr)=CBV_(app) −K _(α) ΔtN  (12), where N is the number of data points in the AIF and Δt is the sampling interval. The corrected flow value is similarly given by: F′=F−K_(a). Note that K_(a) is positive for T2* dominant leakage effects and negative for T1 dominant leakage, and as discussed below both T1 and T2* dominant leakage effects may be expected to occur in DSC-MR imaging of gliomas.

FIG. 4 shows a series of images from a clinical sample case of a grade 2 glioma with strong T₂* dominant leakage leading to an over estimation of CBV using prior art correction methods. The strong contrast agent leakage is apparent on the T₁-weighted post contrast image (image a). The resulting K_(a) leakage map (image b) shows a region of T₂*dominant leakage in the tumor (white circle). The corresponding non-corrected CBV map (image c) shows region of significantly elevated CBV in the same region whereas the leakage corrected CBV map (image d) shows only slightly elevated CBV in the tumor region.

The lack of T₂*-dominant leakage correction could in this case lead to a false positive diagnosis because the artificially high CBV values in the non-corrected image would be more suggestive of a high grade glioma. The corresponding apparent residue functions from normal white matter and tumor is shown in the graph of FIG. 4. The elevated tail of the apparent residue function from the tumor is clearly evident, and a value for K_(a) may be estimated there from using the methods suggested herein.

PV Correction

Optimally, the contrast agent input should be a delta function where the contrast agent in the artery feeding the tissue of interest appears only at one point in time and then disappear. However, because it takes time to inject contrast material and the contrast material is injected in a peripheral vein, and because the body mixes contrast with blood, the actual contrast input function is more like an asymmetric bell curve and is customary estimated by the so-called the arterial input function (AIF). This means that the CTCs not only reflect the tissue perfusion, but also the input function of the contrast agent. In order to derive quantitative estimates of tissue perfusion, AIF is determined and a deconvolution of the CTC's with the AIF is performed.

But, the AIF is usually attenuated due to what is called partial volume effects. With an infinite resolution, reconstructed images should depict the contrast agent distribution uniformly and accurately throughout the field of view. However, because of the limited spatial resolution, “hot” spots (structures) relative to a “cold” background that are smaller than twice the resolution show partial loss of intensity, and the contrast agent concentration around the structure appears to be smeared over a larger area so that the structure appears to be larger and to have a lower activity concentration than it actually has. Similarly, a cold spot relative to a hot background would appear smaller with higher contrast agent concentration. Such underestimation and overestimation of concentration around smaller structures in the reconstructed images is called the partial-volume effect (PVE). As arteries (especially cerebral arteries) are typically smaller than the voxel size in the images, PVE's should be corrected for when making quantitative estimates of tissue perfusion.

A PV correction factor have traditionally been estimated from the ratio of the area under a venous CTC unaffected by PVE (since veins are generally larger in diameter) relative to the area under the CTC of the AIF. This method for PV correction is not very accurate when applied to MRI based images acquired with T₂- or T₂*-weighted sequences. This is due to that the first-pass T₂*-effect in voxels containing only blood is generally so large that complete signal loss occurs, with resulting venous CTC distortion.

Preferably, the automatic partial volume correction applied in an embodiment of the invention uses a novel approach where the pseudo steady-state (immediately following the first-pass phase) part of the respective CTCs of arteries and veins are used rather than the first-pass phase. The reason for doing this is that CTC inside veins are severely distorted by excessive T2* effects in DSC images and it is therefore very hard to determine correctly the area under the first pass curve from a vein. The steady-state effect is, however, not distorted to the same extent and by just measuring the difference in relative steady-state concentration in an artery and a vein we are able to determine the PV correction factor much more accurately. This approach is described in the following with reference to FIG. 1 in the following.

Perfusion image data comprising a signal related to contrast agent concentration as a function of time in voxels during the first and consecutive passages of the contrast agent through the vascular system is accessed or recorded and stored (box 1).

In box 2, AIF and a venous output function (VOF) are preferably be determined automatically. However, representation of contrast agent induced signal strength or other estimations of the contrast agent concentration may also be used.

In box 3, a PV correction factor, f_(pv), is determined as a ratio between parts of the signals following the first passage of the contrast agent from one or more voxels comprising arterial blood and one or more voxels filled with venous blood, respectively.

When f_(PV) has been determined, corrected image data wherein the signal is corrected to take into account PV effects can be calculated using f_(PV) (box 4) and stored and/or presented to a user, box 6. Alternatively or additionally, hemodynamic parameters or a PVE-corrected arterial input function can be calculated using the image data and f_(PV) (box 5) and stored and/or presented to a user, box 5.

The PV correction factor f_(PV) can be determined per slice in the image data. Alternatively, f_(PV) can be determined for the whole imaged volume, or for volumes of interest, such as a tumor region.

The following describes the theory of the PV correction according to an embodiment of the invention in more detail. According hereto, the pseudo-steady-state phase of the CTCs, i.e. the parts of the signals following the first passage of the contrast agent, can be used instead of the first-pass phase. This can be done under the assumption that the venous contrast agent concentration is here sufficiently low to avoid complete signal loss and signal distortion. Assuming that the dose-response is similar in arteries and veins in the steady-state phase and that the measured voxel-wise change in T2* relaxation rate is proportional to contrast agent concentration, the PV correction factor, f_(pv), can be determined as: C _(a) _(—) _(ss)(t)=ƒ_(pv) ·C _(v) _(—) _(ss)(t)  (12) where C_(a) _(—) _(ss)(t) and C_(v) _(—) _(ss)(t) are the steady-state concentrations in the identified arterial and venous voxels, respectively, e.g. the tails of AIF and VOF. It is assumed that the concentration levels in both the arteries and veins follow similar decay curves (or remained approximately constant) so that the mean concentration levels can be used and the PV correction factor can then be determined as the ratio of the mean steady-state concentrations:

$\begin{matrix} {f_{pv} = \frac{{mean}\left( C_{a\_ ss} \right)}{{mean}\left( C_{v\_ ss} \right)}} & (13) \end{matrix}$

Having determined f_(pv), an arterial input function corrected for PV effects can be determined:

$\begin{matrix} {{{C_{a}(t)} = {\frac{1}{f_{pv}}{C_{a}^{PV}(t)}}},} & (14) \end{matrix}$ where C_(a) ^(PV) is the CA concentration in the AIF in the presence of PV effects. Hemodynamic parameters determined from the image data may be corrected in a similar fashion where necessary.

Arterial input functions (AIFs) and Venous output functions (VOFs) are preferably identified using the cluster analysis approach as described for the AIFs later herein, (but using a large CTC FM as the selection criterion for VOFs). Alternatively, one of the several known methods can be used to identify AIF and VOF.

In one embodiment, the part of the signal following the first passage in the AIFs and VOFs can be estimated by first fitting a singly peaked function with zero asymptote, e.g. gamma-variate functions, to the respective CTCs. The CTC tails can be identified as the portion of the curves with amplitude above the corresponding value of the gamma-variate fitted curve (starting at the last time-point), as shown in FIG. 5B. A Fourier based low-pass filter can preferably be applied to the identified AIF and VOF prior to identification of the PV factor in order to improve the stability of the method. A number of specify alternative methods for determining the part of the signal following the first passage are specified in the claims.

When f_(PV) has been determined, a PV corrected signal, or a function derived there from such as the AIF, can be determined and stored and/or presented using the determined PV correction factor, see e.g. Eq. 14 above. Alternatively or additionally, hemodynamic parameters corrected for PV effects can be calculated. As an example, blood volume values can be corrected as: BV=ƒ_(PV)BV^(PV), where BV^(PV) is the blood volume determined in the presence of PV effects.

In a demonstration of the methodology of the embodiment, AIFs from a number of subjects where corrected for PVEs. FIG. 5A shows AIFs automatically detected in each slice and FIG. 5B shows the corresponding average AIF across all slices together with the average venous output function (VOF), which was also based on VOFs determined individually in each slice (not shown). The corresponding gamma variate fitted curves are shown as dotted lines and the intersection points between the AIF/VOF and the gamma variate fitted curves were used to determine the steady-state portion of the respective curves as indicated. Finally the PV correction factor was determined from the difference in the steady state levels of the AIF and VOF, respectively as indicated by the arrow. A single PV correction factor was estimated for all slices based on the average steady-state concentration levels obtained from the identified arterial and venous CTCs. For each subject, the validity of the PV correction factor was assessed (from the criterion that 0<f_(PV)≦1) and any failure to detect at least one pixel representing a valid AIF in each slice was reported during the analysis.

The use of the PVE correction described above in an automated quantitative analysis of hemodynamic properties from contrast agent based perfusion imaging can be found in Bjørnerud and Emblem, A fully automated method for quantitative cerebral hemodynamic analysis using DSC-MRI, Journal of Cerebral Blood Flow & Metabolism (2010), 1-13.

CA Extravasation Correction Applied to Tumor Perfusion Imaging

The following describes estimation of contrast agent extravasation according to an embodiment of the invention and its application to tumor perfusion imaging using MRI. The method according to an embodiment of the invention is also compared to prior art methods for comparison. The correction method described herein is based on the approach where it is assumed that CA extravasation occurs into first into capillary tissue and then into EES. This is an alternative to the approach assuming simultaneous extravasation described previously in the section “Correction for extravascular leakage”.

The following describes an embodiment of the CA extravasation correction method according to the various aspects of the invention. The method enables semi-quantitative determination of the transfer constant and can be used to distinguish between T₁- and T₂*-dominant extravasation effects while being insensitive to variations in tissue mean transit time (MTT). Results in 101 patients with confirmed glioma suggest that leakage-corrected absolute cerebral blood volume (CBV) values obtained with the proposed method provide improved overall survival prediction compared to normalized CBV values combined with an established leakage correction method. Using a standard gradient-echo echo-planar-imaging sequence, about 60% and 10% of the tumors with detectable contrast agent extravasation exhibited mainly T₁- and T₂*-dominant leakage effects, respectively. The remaining 30% of leaky tumors had mixed T₁- and T₂*-dominant effects. Using a MTT-sensitive correction method, our results show that CBV is underestimated when the tumor MTT is significantly longer than MTT in reference tissue.

Contrast agent (CA) extravasation is a general problem for all DSC-based MRI methods used for brain tumor assessment since the kinetic models used explicitly assume that the CA remains in the intra-vascular space for the duration of the dynamic acquisition. Studies suggest that CA leakage can lead to either over- or under-estimation of relative CBV (rCBV) in tumors with blood-brain-barrier breakdown unless specifically corrected for. A correction method where CA extravasation is estimated in each voxel by determining the voxel-wise deviation from a ‘non-leaky’ reference tissue response curve has been proposed. This approach is appealing in that it does not require the use of non-standard imaging sequences or CA injection schemes and the method has been shown to improve the diagnostic accuracy of DSC-MRI in glioma grading (Boxerman et al. 2006). The potential limitation of the method is that the model assumes that MTT and bolus arrival time is the same in tumor and non-pathological tissue. Quarles et al (Quarles et al. 2005) showed, based on simulations and data in a rat gliosarcoma model that this leakage correction method may result in incorrect rCBV values in tumors with significant alteration in the hemodynamic state. Based on this observation they proposed an alternative method where CA extravasation is accounted for by incorporating a leakage term in the tissue residue function, thereby providing an MTT-insensitive estimate of the transfer constant describing the CA flux between the intra-vascular- and extra-vascular extra-cellular space (IVS and EES).

The present invention proposes an alternative approach where the transfer constant is determined directly from the tissue residue function. From this, a direct estimation of perfusion metrics and MTT-insensitive CA extravasation from the resulting tissue residue function can be derived. In a preferred aspect, this may be combined with a fully automated approach for quantitative DSC-MRI incorporating automatic slice-wise detection of the AIF and partial volume (PV) correction.

Theory

Estimation of Tumor Hemodynamic Parameters in the Presence of CA Extravasation

A correction method is described by Boxerman et al (Boxerman et al. 2006) where CA extravasation is estimated in each voxel by determining the voxel-wise deviation from a ‘non-leaky’ reference tissue response curve:

$\begin{matrix} {{\Delta\; R\; 2^{*}(t)} \approx {{K_{1} \cdot \overset{\_}{\Delta\; R\; 2^{*}(t)}} - {K_{2}{\int_{0}^{t}{\overset{\_}{\Delta\; R\; 2^{*}\left( t^{\prime} \right)}\ {\mathbb{d}t^{\prime}}}}}}} & (15) \end{matrix}$ where ΔR2*(t) is the measured CA induced change in transverse relaxation rate (1/T₂*) in the presence of CA extravasation, ΔR2*(t) is the average ΔR2*(t) in voxels with no CA extravasation, K₁ and K₂ are scaling constants for relative blood volume and permeability, respectively. The negative sign of K₂ is due to the assumed T₁-dominant CA relaxation effect in the EES. Relative CBV is given by the area under the first-pass response, and it thus follows that the leakage corrected rCBV is given by:

$\begin{matrix} {{rCBV}_{corr} = {{rCBV} + {K_{2}{\int_{0}^{T}\ {{\mathbb{d}t^{''}}{\int_{0}^{t^{''}}{\overset{\_}{\Delta\; R\; 2^{*}}\left( t^{\prime} \right)\ {\mathbb{d}t^{\prime}}}}}}}}} & (16) \end{matrix}$

This approach will be used as the reference correction method in the current work. One potential limitation of this method is that it explicitly assumes that MTT in a leaky voxel is identical to the MTT of the mean tissue response curve (Quarles et al. 2005). This can be seen from Equation 15 because, in the absence of extravasation, any given response curve should be related to the reference curve by a single scaling constant (K₁). Any deviations in MTT (or CA delay) would thus introduce an incorrect non-zero value of K₂.

An alternative approach accounting for variations in tissue MIT is to estimate CA extravasation from the tissue residue function obtained following AIF deconvolution. In the absence of CA extravasation, tissue flow can be estimated from the convolution integral:

$\begin{matrix} {{C_{t\_ iv}(t)} = {f{\int_{0}^{t}{{R(t)}{C_{p}\left( {t - \tau} \right)}{\mathbb{d}\tau}}}}} & (17) \end{matrix}$ where C_(p) is the tracer concentration in plasma and C_(t) _(—) _(iv), is the tracer concentration in tissue (confined to the IVS), R(t) is the tissue specific residue function and f is tissue flow (in units of 1/s). Given that CA concentration in blood and tissue can be determined, f and R(t) can be estimated by deconvolution, and perfusion (in units of mL blood/100 g/min) is then given by:

$\begin{matrix} {{CBF} = {\frac{H_{c}}{\rho}f}} & (18) \end{matrix}$ where ρ is tissue density and H_(c)=1−Hct_(art)/1−Hct_(cap) takes into account differences in hematocrit values in large vessels and capillaries. The MIT is given by the area under the residue function and, in the absence of CA extravasation, CBV can then be estimated from the central volume principle:

$\begin{matrix} {{CBV} = {{{CBF} \cdot {MTT}} = {\frac{H_{c}}{\rho}f{\int_{0}^{\infty}{{R(t)}\ {\mathbb{d}t}}}}}} & (19) \end{matrix}$

If the tracer is not confined to the IVS, CA extravasation can be expressed in terms of a two compartment model:

$\begin{matrix} {{C_{t\_ ev}(t)} = {K^{trans}{\int_{0}^{t}{{{\exp\left( {{- {K^{trans}\left( {t - \tau} \right)}}/v_{e}} \right)} \cdot {C_{p}(t)}}\ {\mathbb{d}\tau}}}}} & (20) \end{matrix}$ where K^(trans) is the transfer constant describing the CA flux from the IVS to the EES, ν_(e) is the leakage space per unit volume and C_(t) _(—) _(ev) is tracer concentration in the EES. It is noted, that the reflux rate constant k_(ep) previously used to quantify a rate of contrast agent reflux from EES to IVS elsewhere (under the assumption that CA leaks into capillary tissue and EES simultaneously). From conservation of mass, the constant k_(ep) is related to K^(trans) by the expression: k_(ep)=K^(trans)/V_(e) where V_(e) is the fractional distribution volume of the contrast agent in the EES. For clarity and compliance with literature, k_(ep) will be replace by K^(trans)/V_(e) in the following.

In order to estimate both perfusion and permeability from a single acquisition, a combined model of the two processes is needed. We base our combined analysis approach on the adiabatic approximation to the tissue homogeneity model. Here, the intra-vascular response is modelled as a function of both time and distance along the capillaries and it is assumed that the dynamic time course is separable into an early (fast) vascular phase followed by a (slow) extravasation phase. The tissue response, including both the intra-vascular- and extra-vascular responses can then be expressed as:

$\begin{matrix} {{C_{t\_ m}(t)} = {{f{\int_{0}^{t}{{R(t)}{C_{p}\left( {t - \tau} \right)}\ {\mathbb{d}\tau}}}} + {K^{trans}{\int_{T_{c}}^{t^{\prime}}{{{\exp\left( {{- {K^{trans}\left( {\tau - T_{c}} \right)}}/v_{e}} \right)} \cdot {C_{p}\left( {t^{\prime} - \tau} \right)}}\ {\mathbb{d}\tau}}}}}} & (21) \end{matrix}$ where T_(c) is the capillary transit time of the CA so that t<T_(c) and t′≧T_(c). The combined residue function H(t) scaled by flow and the extravasation transfer constant can then be expressed as: H(t)≈ƒ·R(t) 0≦t<T _(c) H(t)≈K ^(trans)·exp(−K ^(trans)(t−T _(c))/ν_(e)) t≧T _(c)  (22)

Complete separation of the intra-vascular- and extravasation phase using this model requires R(t) to be a box function so that R(t)=1 for 0≦t<T_(c) and R(t)=0 for t≧T_(c). However, since the intra-vascular residue function is in reality a monotonically decreasing probability function the two phases will overlap and T_(c) is an average transit time (MTT) for all capillary paths. However, for t>>T_(c), H(t) is dominated by the leakage term and by further assuming limited reflux within the measurement time, T_(N), so that K^(trans)T_(N)/v_(e)<<1, we get: H(t)≈K ^(trans) t>>T _(c)  (23) Dose Response Considerations

In DSC-MRI, CA concentration can only be estimated in relative terms through measurements of change in transverse relaxation rate (ΔR2* or ΔR2) which in turn is estimated from measured change in MR signal intensity (SI). In single shot GRE-EPI sequences used in DSC-MRI, the SI can be approximated by the steady-state expression:

$\begin{matrix} {{{SI}(C)} = {{M_{0}\frac{{\sin(\alpha)}\left( {1 - {\exp\left( {{{- {TR}} \cdot R}\; 1(C)} \right)}} \right.}{1 - {{\cos(\alpha)}{\exp\left( {{{- {TR}} \cdot R}\; 1(C)} \right)}}}{\exp\left( {{{- {TE}} \cdot R}\; 2^{*}(C)} \right)}} = {M_{0}E\; 1{(C) \cdot {\exp\left( {{{- {TE}} \cdot R}\; 2^{*}(C)} \right)}}}}} & (24) \end{matrix}$ where M₀ is proportional to the equilibrium magnetization, C is the CA concentration, R1, R2* are T₁- and T₂* relaxation rates, respectively, TE is the echo time and α is the flip angle. The change in SI due to CA induced increase in relaxation rates can then be expressed as:

$\begin{matrix} {{\frac{1}{TE}\left\lbrack {\ln\left( \frac{{SI}(0)}{{SI}(C)} \right)} \right\rbrack} = {{{\Delta\; R\; 2^{*}(C)} - {\frac{1}{TE}{\ln\left( \frac{E\; 1(C)}{E\; 1(0)} \right)}}} = {\Delta\;{{R2}_{app}^{*}(C)}}}} & (25) \end{matrix}$ where ΔR2* is the change in T₂* relaxation rate, ΔR2*_(app) is the measured apparent change in ΔR2* including T₁-effects and E1(C)>E1(0). In DSC imaging, the T₁-term in Equation 25 is commonly assumed to be negligible compared to the much stronger T₂* relaxation effects for an intra-vascular CA distribution. In the case of CA extravasation T₁-relaxation effects may become significant due to a reduction in CA compartmentalization (reduced T₂*-relaxation) combined with increased distribution volume and water access to the paramagnetic centre of the CA. Hence, the extravascular CA induced signal change is more difficult to predict, and both T₁- and T₂* effects may dominate when CA is present in the EES.

From this, it cannot be assumed that the transfer constant measured from a single echo DSC-MRI acquisition reflects the underlying K^(trans). We therefore distinguish between the apparent transfer constant, K_(a), estimated through measurements of ΔR2* combined with the proposed models, and the true transfer constant K^(trans) as defined in Equation 20. Using this notation, Equation 7 can be written in matrix notation in terms of the measured changes in T₂* relaxation rates as: Y=A·h   (Tb 26 where

$\begin{matrix} {Y = \begin{bmatrix} {\Delta\; R\; 2_{t}^{*}\left( t_{0} \right)} \\ {\Delta\; R\; 2_{t}^{*}\left( t_{1} \right)} \\ \vdots \\ {\Delta\; R\; 2_{t}^{*}\left( t_{N - 1} \right)} \end{bmatrix}} & (27) \\ {A = {\Delta\;{t \cdot \begin{bmatrix} {\Delta\; R\; 2_{a}^{*}\left( t_{0} \right)} & 0 & 0 & 0 \\ {\Delta\; R\; 2_{a}^{*}\left( t_{1} \right)} & {\Delta\; R\; 2_{a}^{*}\left( t_{0} \right)} & \ldots & 0 \\ \vdots & \vdots & \vdots & \vdots \\ {\Delta\; R\; 2_{a}^{*}\left( t_{N - 1} \right)} & {\Delta\; R\; 2_{a}^{*}\left( t_{N - 2} \right)} & \ldots & {\Delta\; R\; 2_{a}^{*}\left( t_{0} \right)} \end{bmatrix}}}} & (28) \end{matrix}$ and

$\begin{matrix} {h = {{r + e} = {{{f\begin{bmatrix} {R\left( t_{0} \right)} \\ {R\left( t_{1} \right)} \\ \vdots \\ {R\left( t_{C} \right)} \\ 0 \\ 0 \\ \vdots \\ 0 \end{bmatrix}} + {K_{a}\begin{bmatrix} 0 \\ 0 \\ \vdots \\ 0 \\ 1 \\ {\exp\left( {{- K^{trans}}\Delta\;{t/v_{e}}} \right)} \\ \vdots \\ {\exp\left( {{- {K^{trans}\left( {N - 1} \right)}}\Delta\;{t/v_{e}}} \right)} \end{bmatrix}}} = \begin{bmatrix} {H\left( t_{0} \right)} \\ {H\left( t_{1} \right)} \\ \vdots \\ \vdots \\ \; \\ \; \\ \vdots \\ {H\left( t_{N - 1} \right)} \end{bmatrix}}}} & (29) \end{matrix}$ where Δt is the sampling interval, N is the number of data-points, t_(c) is the time index corresponding to T_(c), ΔR2_(t)* is the apparent change in R2* in tissue in the presence of T₁-effects and extravasation (Equation 25) and ΔR2_(a)* is the corresponding change in R2* in blood. Equation 26 can be solved for h using standard matrix inversion methods like singular value decomposition (SVD) and K_(a) is then approximated from the tail of H(t) following the assumptions leading up to Equation 23.

The apparent blood volume measured in a leaky voxel is given by the area under H(t), which can be expressed in terms of the intra-vascular (v_(i)) and extra-cellular (v_(e)) volume fractions as follows:

$\begin{matrix} {{v_{T} \approx {{f{\int_{0}^{T_{c}}{{R(t)}\ {\mathbb{d}t}}}} + {K_{a}{\int_{T_{c}}^{\infty}{{\exp\left( {{- {K^{trans}\left( {t - T_{c}} \right)}}/v_{e}} \right)}{\mathbb{d}t}}}}}} = {v_{i} + v_{e}}} & (30) \end{matrix}$

The intra-vascular blood volume (in units of mL blood/100 g) is then given by:

$\begin{matrix} {{CBV}_{i} = {\frac{H_{c}}{\rho}\left( {v_{T} - v_{e}} \right)}} & (31) \end{matrix}$

Since we have assumed negligible CA reflux within the total sampling time, v_(e) cannot be estimated but the error in CBV_(i) due to CA extravasation can then be estimated from the approximation H(t)≈K_(a) for t>>T_(c) so that the leakage corrected intra-vascular blood volume is given by: CBV_(corr)=CBV_(app) −K _(α) Δt(N−N _(c))/ρ;NΔtK ^(trans)/ν_(e)<<1  (32) where CBV_(app) is the apparent CBV value measured by Equation 19 and N_(c) is the time index corresponding to T_(c). T_(c) is unknown and tissue dependent but may be estimated by fitting the initial portion of H(t) to an appropriate parametric function. CBF is not affected by CA extravasation effects since H(t)=fR(t) (t<<T_(c)) is not dependent on K_(a). Methods Patient Material

Study approval was obtained from the Regional Medical Ethics Committee and patients were included only if informed consent was signed. A total of 101 patients (51 males, mean age 51 years, range 8-79 years) with confirmed glioma, selected from an ongoing prospective tumor perfusion study were included in the analysis. The histopathological diagnosis of the included patients is specified in a previous study (Bjornerud and Emblem 2010), and for the current work the patients were divided into two groups where glioma grades I and II were grouped as low grade gliomas (LGG) and glioma grades III and IV were grouped as high grade (HGG).

MR Imaging

Imaging was performed at 1.5 Tesla (Siemens Sonata, Symphony or Avanto, Siemens AG, Erlangen, Germany), using an 8-channel-(Symphony/Sonata) or a 12-channel (Avanto) head-coil. DSC MRI was performed using a GRE-EPI sequence acquired during CA administration. The DSC imaging parameters were: TR/TE/flip angle 1430 ms/46 ms/90°, bandwidth 1345 Hz/pixel (12 axial slices) or 1720/48, bandwidth 1500 Hz/pixel (14 axial slices), field of view 230×230 mm², voxel size 1.8×1.8×5 mm³, inter-slice gap 1.5 mm. For each slice, 70 images were recorded at intervals equal to the repetition time (TR). After eight time-points, 0.2 mmol/kg of the CA gadobutrol (Gadovist™, Bayer Schering Pharma AG, Berlin, Germany) was injected at a rate of 5 mL/s, immediately followed by a 20 mL bolus of saline (B. Braun Melsungen AG, Melsungen, Germany), also at 5 mL/s. The image protocol included axial T₂-weighted fast spin-echo (FSE) images (TR/TE=4000 ms/104 ms), coronal fluid attenuated inversion recovery (FLAIR) images (TR/TE=9050 ms/114 ms and TI=1500 ms) and axial T₁-weighted SE images (TR/TE=500 ms/7.7 ms) obtained before and after i.v. CA injection. The voxel size was 0.45×0.45×5 mm³ with 19 slices for the T₂- and T₁-weighted images and 0.9×0.9×5 mm³ with 25 slices for the FLAIR images.

Data Analysis

Perfusion Analysis and Extravasation Correction

The proposed extravasation correction methods was compared to the reference method of Boxerman et al (Boxerman et al. 2006, or U.S. Pat. No. 6,807,441), referred to as Method I. Different from the original implementation, the constant K₂ (Equation 15) was allowed to assume both positive and negative values in order to account for the possible presence of both T₁- and T₂*-dominant relaxation effects during CA extravasation. In the proposed alternative method (denoted Method II) the apparent transfer constant K_(a) was determined directly from the tail of the residue function as outlined in the Theory section. Method I was used only to correct relative CBV values normalized to unaffected white matter whereas Method II provided absolute estimates of CBF and leakage corrected CBV and MTT from the residue function. The residue function was determined on a pixel-by-pixel basis (or from simulated response-curves) using iterative Tikhonov-regularized SVD (iTrSVD) deconvolution. The intravascular residue function R(t) was estimated by fitting the initial portion (first five time points) of H(t) to a Lorentzian function of the form:

$\begin{matrix} {{R(t)} = \left\lbrack {1 + \left( \frac{\pi \cdot t}{2T_{c}} \right)^{2}} \right\rbrack^{- 1}} & (33) \end{matrix}$ where T_(c) is the intravascular transit time which was then used as an estimate of the cut-off point between the intravascular phase and the extravasation phase corresponding to the tail part (Equation 22). The curve fit was performed using a Levenberg-Marquardt non-linear least squares fitting procedure. The Lorentzian function provided excellent goodness of fit to actual residue functions obtained in unaffected white and grey matter (data not shown). Simulations

Simulations were performed to investigate the validity of the two extravasation correction methods under different hemodynamic conditions and to assess the sensitivity of the models to variations in underlying tissue relaxation properties and sequence parameters. For all simulations the AIF was modelled as a gamma-variate function, but with an additional exponential term to model steady-state effects:

$\begin{matrix} {{{Ca}(t)} = {{\left( {t - T_{0}} \right)^{a}{\exp\left( {- \frac{t - T_{0}}{b}} \right)}} + {{Ca}_{ss}\left( {1 - {{\exp\left( {- \frac{t - T_{0{ss}}}{\beta}} \right)}{\exp\left( {- \frac{t - T_{0{ss}}}{T_{el}}} \right)}}} \right.}}} & (34) \end{matrix}$ where a, b β are curve shape constants, T₀ is the CA arrival time, T_(0ss) is a time delay constant for the steady-state effect, Ca_(ss) is the steady-state CA concentration and T_(el) is the plasma elimination half-life of the CA. The constants were chosen such that Ca_(max)=7 mM and Ca_(ss)=1 mM. A Lorentzian intra-vascular residue function (Equation 33) was used for all simulations. Dependence of K_(a) on Transverse Relaxivity and Sequence Parameters

The concentration time curves C_(t) _(—) _(iv)(t) and C_(t) _(—) _(ev)(t) were estimated from the AIF by convolution (Equations 17 and 20) for given values of MTT, CBF, K^(trans) and v_(e) and the corresponding relaxation rates changes in the respective compartments were calculated as described below. Signal changes corresponding to the estimated CA induced relaxation rate changes were then calculated using the expression for steady-state GRE signal behaviour (Equation 25) and the corresponding changes in apparent R2* relaxation rates were calculated from the simulated signal changes, assuming negligible T₁-effects:

$\begin{matrix} {{\Delta\;{{R2}_{app}^{*}(C)}} = {\frac{1}{TE}{\ln\left( \frac{{SI}(0)}{{SI}(C)} \right)}}} & (35) \end{matrix}$ R2*_(app) in tissue was then deconvolved with the AIF R2* response curve in order to estimate the residue function measured in the presence of extravasation and tissue relaxation effects. Finally, K_(a) was extracted from the residue function using Method II as described in the Theory section.

The tissue T₁- and T₂*-relaxation rates were estimated by assuming linear dose-response functions: R2*(C)=R2*(0)+r2·C R1(C)=R1(0)+r1·C  (36) where r1 and r2 are the T₁- and T₂*-CA relaxivities, respectively in a given tissue compartment and R1(0) and R2*(0) are the relaxation rates in the absence of CA. Change in tissue T₁-relaxation was assumed to be a function of extra-vascular CA concentration only, assuming the intra-vascular T₁-relaxation contribution in tissue to be negligible. The CA-induced change in R2* relaxation rates were assumed to be a linear combination of the intra-vascular and extra-vascular contributions: ΔR2_(t)*(C _(ev) ,C _(iv))=ΔR2_(ev)*(C _(ev))+ΔR2_(iv)*(|C _(iv) −C _(ev)|)  (37)

The dependence of ΔR2*_(iv) on ΔC=|C_(iv)−C_(ev)| is due to the fact that ΔR2*_(iv) is proportional to the susceptibility difference (ΔX) between the two compartments and Δχ∝ΔC. The effect of variations in extra-vascular structure and volume was simulated by varying the effective transverse relaxivity, r2_(ev) in the EES. The value of r2_(ev), was initially set equal to the dipolar value as obtained in a completely homogeneous solution (r2=5.3 mM⁻¹s⁻¹). This was assumed to be the lower limit in tissue with complete loss of cellular integrity. In tissue with intact cell membranes, r2_(ev) will be higher due to field perturbations at the intra- and extra-cellular interface. The effect of increasing degree of compartmentalization was simulated by a step-wise increasing of r2_(ev) up to a maximum value of 30 mM⁻¹s⁻¹. For the intra-vascular contribution, r2_(iv)=44 mM⁻¹s⁻¹ was used, a value which was previously found to be valid for both grey and white matter in the brain at 1.5 T.

A linear dose-response was also assumed for the AIF. Although studies have shown that R2* relaxation in large arteries is quadratically dependent on the CA concentration, the automated AIF determination implemented in the current work tends to select voxels located outside the large arteries where a linear R2* dose response and absence of T₁ relaxation effects can be assumed. The tissue contribution to the AIF was assumed to be negligible and an arterial R2* relaxivity r2_(a) of 8 mM⁻¹s⁻¹ was used. The value of r2_(a) was taken as being close to the linear component of the intra-vascular relaxivity previously described, a value which was also found to give AIF R2* response curves in good agreement with results in patient data. For T₁-relaxivity in the EES, r1=4.2 mM⁻¹s⁻¹ was used.

K_(a) estimated from the above method was compared to the actual K^(trans) over a relevant range of K^(trans) (corresponding to extraction fractions 0≦E≦0.5 where E=K^(trans)/f). Sequence parameters were kept constant except for the flip angle that was varied between 30° and 90°. The effect of using a pre-dose was also simulated by estimation of the respective CA concentrations in all compartments following a first injection, and using these concentration values as baseline values for a second injection. The following additional parameters were fixed for all simulations: TR/TE=1500 ms/45 ms, CBF=80 mL/100 g/min and MTT=5 s.

MTT Dependence

Using pre-defined values of CBF, MTT and K_(a) tissue response curves were generated according to Equations 27-29. Gaussian noise corresponding to an SNR of 50 in the raw data was added. Defining the apparent extraction fraction as E_(a)=K_(a)/f, simulations were performed with E_(a)=0.1 and E_(a)−0.1 to model both T₁-(E_(a)<0) and T₂*-(E_(a)>0) dominant extravasation effects. The simulated leakage affected response curves were then used to estimate K_(a) or K₂ and the corresponding leakage corrected perfusion metrics obtained using the two correction methods where compared to the same values in the absence of extravasation. When applying correction Method I to the simulated data, a reference tissue response curve with E_(a)=0, MTT=5 s and CBF=40 mL/100 g/min was assumed and a leakage corrected response curve was generated from Equation 15. When varying MTT, CBF was kept constant at 80 mL/100 g/min so that CBV varied as a function of MTT. Finally, in the case of no extravasation, MTT varied between 0.5 and 4 times the corresponding MTT in reference tissue (0.5<nMTT<4). For a given nMTT, the error in K₂ (i.e. deviation from zero) and corresponding error in the leakage corrected rCBV value was estimated. The error in rCBV was estimated as the percent difference between rCBV values obtained when applying leakage correction according to Method I compared to the values obtained without applying leakage correction.

All data simulations were performed in Matlab 2007a (MathWorks, Natick, Mass.)

Comparison of Extravasation Correction Methods in Patient Data

The sensitivity of correction Method I to variations in MTT was tested based on pixel-wise analysis in selected tumors (with tumor MTT values deviating from MTT in non-pathological tissue) and compared to the expected results based on the simulations. Leakage corrected MTT values (obtained using correction Method II) were extracted from each voxel within the tumor region-of-interest (ROI) and normalized to the MTT derived from a mask of unaffected white and grey matter to yield nMTT values which were correlated to the corresponding pixel-wise K₂ and K_(a) values. In order to estimate the error in K₂ as a function of nMTT, K_(a) was assumed to be linearly related to K₂ for values of nMTT close to unity. Selecting only tumor pixels with nMTT≈1 the linear correlation coefficient was then estimated so that K₂ ^(est)=αK_(a). Under the assumption that K_(a) is independent of nMTT the error in K₂ as a function of nMTT was then ΔK₂=αK_(a)−K₂. The same tissue mask used to extract normalized MTT values was used to determine the reference tissue response curve when estimating K₂ according to Method I (Equation 15) so that for pixels with nMTT≈1 it would be expected that 1K₂≈0. Finally, under the assumption that corrected CBV obtained from Method II (CBV(II)) is independent of nMTT, the percent difference between CBV(II) normalized to unaffected white matter and nCBV(I) was plotted as function of nMTT.

Tumor Segmentation

Using the anatomical MR images, binary glioma ROIs were derived from each MR image slice using an automatic tumor segmentation routine based on knowledge-based Fuzzy c-means (FCM) clustering.

Parametric Image Generation

Applying the two correction methods, parametric leakage maps were generated where T₁-dominant and T₂*-dominant leakage constants (K₂, Method I or K_(a), Method II) were rendered with different color palettes (blue colors for positive T₂*-dominant leakage and red colors for negative T₁-dominant leakage). Positive and negative K₂- and K_(a) values were identified in the segmented tumor volume and analyzed separately. When differentiating T₁- and T₂*-dominant leakage effects, the transfer constants are referred to as K_(a)(T₁) and K_(a)(T₂*) respectively for T₁- and T₂*-dominant effects.

All image processing methods, except for the tumor segmentation method were performed using a modified version of nordicICE (NordicImagingLab AS, Bergen, Norway). Tumor segmentation was performed in Matlab R2007a (MathWorks, Natick, US).

Statistical Comparisons

Group differences between HGG and LGG for the derived hemodynamic parameters were tested using Mann-Whitney U-test with a significance level of 0.01. Using normalized histogram peak values derived from the corrected CBV values from tumor segments, logistic regression was used in combination with available survival data to derive Kaplan-Meier survival curves with respect to separating a ‘high-risk group’ (survival<1 year after MRI exam) from a ‘low-risk group’ (survival>1 year) regardless of histopathological grading. Statistical analysis was performed using SPSS 17 (SPSS, Inc., Chicago, Ill., USA).

Results

Simulations

FIGS. 6A-C show the results of the simulation of the correlation between K_(a) and K^(trans) as function of flip angle (6A), extra-vascular transverse relaxivity (r2_(ev)) (6B) and presence or absence of pre-dose (6C). K_(a) was generally found to be a non-linear function of K^(trans). At low values of K^(trans) and r2_(ev), combined with large flip angles, K_(a) was initially negatively related to K^(trans) due to a T₁-dominant leakage effect. At higher K^(trans) values, K_(a) was almost independent of K^(trans) for low values of r2_(ev). With increasing r2_(ev) and reduction in flip angle, K_(a) became increasingly positive (T₂* dominant leakage) and was a positive function of K^(trans). Use of pre-dose resulted in mainly T₂*-dominant leakage effects and, expect for an initial negative dip, K_(a) being a positive function of K^(trans) even for high flip angles and low r2_(ev) values.

FIGS. 7A and B show the correlations between the estimated CBV and MTT after extravasation correction using the two correction methods compared to actual- and uncorrected values. Method II was able to reproduce the reference values after correction for both perfusion metrics, whereas Method I resulted in an increasing under-estimation of CBV and MTT with increasing MTT and CBV values. Uncorrected CBV and MTT values were significantly over-estimated for T₂*-dominant leakage (FIG. 7A) and under-estimated for T₁-dominant leakage (FIG. 7B). CBF was not significantly affected by extravasation effects (data not shown).

FIGS. 8A and B show the simulated error in K₂ (ΔK₂) as a function of nMTT (8A) and the corresponding error in rCBV (ΔrCBV) in percent after correction using Method I (8B) in the situation of no CA extravasation (E=0). ΔK₂ increased quadratically with increasing nMTT and nMTT>1 resulted in a linear increase in the relative under-estimation in rCBV due to an artificially positive value of K₂. The error for nMTT<1 was small for both rCBV and K₂.

Patient Data

About 60% of all tumors with detectable CA extravasation exhibited predominantly T₁-enhancing leakage effects (defined as >70% of tumor voxels with non-zero K_(a) having K_(a)<0). About 10% of the tumors exhibited predominantly T₂*-enhancing leakage and the remaining 30% had an approximately equal mix of T1- and T₂*-dominant leakage effects. FIG. 9A shows two/glioblastoma cases demonstrating T₁-dominant (left) and T₂*-dominant extravasation effects. FIG. 9B shows the corresponding dose-response curves and residue functions for the same two sample cases. As predicted by theory and simulations, the T₁-dominant leakage resulted in a negative tail in the residue function and T₂*-dominant leakage resulted in a positive tail.

Two selected sample cases demonstrating the effect of elevated tumor MIT values are shown in FIG. 10. The top row shows a grade III anaplastic astrocytoma with significant elevation of nMTT in tumor resulting in apparent T₂*-dominant leakage as seen in the K₂-map in spite of absence of visible contrast enhancement in the T₁-weighted image after CA administration. The artificial T₂*-dominant leakage resulted in lower nCBV in tumor compared to CBV obtained with Method II. The bottom row shows a glioblastoma with elevated MTT values in the tumor rim resulting in over-estimation of K₂ and under-estimation of nCBV in areas of elevated MTT values.

FIGS. 11A-C show pixel-wise analysis of error in K₂ and rCBV as function of nMTT for two cases selected based on the presence of a large range of nMTT values in tumor. The left column (11A) shows the correlation between K_(a) and K₂ for all pixels with 0.9<nMTT<1.1. A significant and similar linear correlation was observed between K_(a) and K₂ for voxels with nMTT≈1 in both cases and the regression coefficients could therefore be used to determine the residual error in K₂ as a function of nMTT. Both cases showed an increase in ΔK₂ (centre column, 11B) and a negative increase in percent difference between nCBV(I) and nCBV(II) (right column, 11C) with increasing nMTT. ΔK₂ had zero crossing at about nMTT=1, in good agreement with simulations (FIGS. 8A-B).

The mean leakage corrected whole tumor CBV (+/−SD) was 2.1±0.8 mL/100 g and 3.9±1.7 mL/100 g, respectively in LGG and HGG (P<0.001). Using the same correction method, both mean MIT and K_(a)(T₂*) was significantly higher (P<0.001) in HGG compared to LGG. The average MTT in HGG was 5.6±1.5 s and 4.0±1.0 s in LGG. Mean K_(a)(T₂*) was 0.17±0.08 min⁻¹ in HGG and 0.11±0.08 min⁻¹ in LGG. K_(a)(T₁) was not significantly different in HGG and LGG. The K_(a) values obtained in vivo were in the same range as those obtained in the simulations (FIGS. 6A-C). For the Kaplan-Meier analysis, the log-rank (Mantel-Cox Chi-Square) values describing the difference between the low- and high-risk survival curves were higher for correction Method II than for Method I (23.69; P<0.001 and 16.46; P<0.001, respectively). The Kaplan-Meier survival curves are shown in FIG. 12.

The above method enables estimation of CA extravasation and multiple perfusion metrics directly from the tissue residue function. The development of the method was motivated by limitations in existing methodology and an identified need for quantitative assessment of tumor hemodynamic properties. Although a post processing based method for leakage correction is established (Boxerman et al. 2006), two important limitations of this reference correction method were identified: 1) the method is sensitive to deviations in tumor MTT compare to reference tissue MTT and 2) the method only corrects for T₁-dominant leakage. The latter point can easily be overcome by allowing the apparent transfer constant (K₂) to assume both positive and negative values. The MTT sensitivity is, however, inherent in the method and we show through simulations and in patient data that elevated MTT in tumor tissue may lead to underestimation of rCBV as a result of incorrect estimation of K₂. Given that MTT was found to be significantly higher in HGG than in LGG, our results suggest that the reference method may underestimate rCBV in tumors even when leakage correction is performed. The proposed correction method providing absolute leakage corrected CBV values was found to provide improved survival prediction compared to the reference correction method of Boxerman et al applied to normalized CBV values. The survival analysis was based on whole tumor CBV histogram analysis, an approach previously shown to robustly predict outcome from automatically generated tumor ROIs.

The problem of MTT sensitivity of the reference method has previously been pointed out by other investigators. Quarles et al (Quarles et al. 2005) proposed an alternative MIT insensitive correction method which also relies on AIF deconvolution. Different from the method of Quarles et al we aimed at estimating all hemodynamic parameters directly from the leakage corrected tissue residue function, thereby avoiding the step of re-generating a leakage corrected tissue response curve. Although no gold standard currently exists, alternative models providing combined assessment of both perfusion and CA extravasation have been proposed.

The model assumptions used in the correction method discussed here deviates somewhat from the model presented previously where capillary perfusion and EV leakage were assumed to occur as two parallel processes originating from the same arterial source. Although the current model probably better describes the underlying kinetics of the CA the estimation of K_(a) is in practice identical for the two models and the CBV correction differs only by the non-zero offset value N_(c) (Equation 32) in the modified model.

The proposed method relies on accurate estimation of the tissue residue function which requires both robust estimation of the AIF and stable deconvolution in the presence of noise. Given the recent advent of automated AIF detection methods (see e.g. Mouridsen et al. 2006), it is expected that much of the current user-dependence in associated with AIF determination can be eliminated. The need of the method to identify a ‘steady-state’ level in a noisy and generally oscillating residue function is also a challenge. We minimized oscillations by employing an iterative Tikhonov regularization based SVD deconvolution method and were able to obtain robust estimates of both T₁-dominant and T₂*-dominant leakage effects using this approach.

Computer simulations were used to investigate the relationship between the measured apparent rate constant K_(a) and K^(trans). Although the performed simulations make several simplifying assumptions regarding in vivo relaxation effects, the results clearly suggest that the apparent transfer constant estimated from DSC-MRI is generally not linearly related to the underlying permeability surface area product of the tumor tissue, even when extravasation is permeability limited (CBF>>PS). This lack of linear correlation is partly due to the complex relationship between CA concentration in tissue and the measured change signal intensity and corresponding transformation to apparent transverse relaxation rates. The presence of both T₁- and T₂*-relaxation effects in the EES can result in both positive and negative apparent rate constants depending on the underlying tissue properties as well as sequence parameters. The presence of both these effect was confirmed in the patient data. An additional source of non-linearity is due to the assumption of negligible CA reflux. For the higher K^(trans) values tested in these simulations the required condition that K^(trans)T_(N)/v_(e)<<1 is clearly violated, resulting in an under-estimation of K_(a) at high K^(trans) values. An improved model where the tail of H(t) is not assumed to be a constant but is fitted to the full exponential function (Equation 29) is therefore warranted and may provide a better estimate of K^(trans). However, even with improved kinetic models, absolute estimations of K^(trans) from DSC acquisitions will remain challenging due to an unpredictable- and generally non-linear dose response in DSC-MRI.

The simulations confirmed that the use of a pre-dose reduces T₁-effects and gives predominantly positive K_(a) values except at very low K^(trans) where an initial negative ‘dip’ was observed. The presence of this initial ‘inverted’ K_(a) response at low K^(trans) values could be a potential challenge but this effect needs to be confirmed in clinical data where a pre-dose is used. In the current study no pre-dosing and a large flip angle of 90 deg was used, both factors resulting in an increased sensitive to T₁-dominant leakage effects. Although K_(a) should be expected to correlate with tumor grade, such a correlation was only observed for K_(a)(T₂*). The lack of correlation of K_(a)(T₁) with tumor grade may be due to the non-linear dependence, and to a certain degree the non-dependence of K_(a)(T₁) and (K_(a)<0) on K^(trans), as seen in FIGS. 4A and 4B. Given the results of the simulations showing that transition from T₁- to T₂*-dominant leakage depends strongly on the effective transverse relaxivity in the EES, it could be hypothesized that the presence or absence of the two competing leakage effects may convey relevant information concerning the extra-vascular tissue structure within the tumor. This effect could thus be a potential marker for assessment of treatment response by for instance monitoring of changes in the relative K_(a)(T₁)/K_(a)(T₂*) fraction during treatment. This observation warrants further investigation.

In summary, the presented extravasation correction method enables robust correction for both T₁- and T₂*-dominant leakage effects independent of the MTT of the target tissue. The method can be combined with automated methods for AIF detection, providing estimates of multiple hemodynamic parameters without, user interaction.

Although the present invention has been described in connection with the specified embodiments, it should not be construed as being in any way limited to the presented examples. The scope of the present invention is to be interpreted in the light of the accompanying claim set. In the context of the claims, the terms “comprising” or “comprises” do not exclude other possible elements or step. Also, the mentioning of references such as “a” or “an” etc. should not be construed as excluding a plurality. In general, and specifically in the claims, “or” should be interpreted as a non-exclusive or. The use of reference signs in the claims with respect to elements indicated in the figures shall also not be construed as limiting the scope of the invention. Furthermore, individual features mentioned in different claims, may possibly be advantageously combined, and the mentioning of these features in different claims does not exclude that a combination of features is not possible and advantageous.

REFERENCES

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The invention claimed is:
 1. A method for estimating contrast agent extravasation in contrast agent based perfusion imaging methods to be performed by an electronic processor, the method comprising: accessing perfusion image data comprising a signal related to contrast agent concentration as a function of time in a voxel during the first and consecutive passages of the contrast agent through the vascular system; representing the signal by a convolution, R_(ps)′(t)

C_(p)′(t), of an apparent residue function, R_(ps)′(t), and an estimated contrast agent concentration in plasma, C_(p)′(t), and determining the apparent residue function R_(ps)′(t) by deconvolution of the signal with C_(p)′(t); estimating a first leakage rate constant K_(a) from a tail part of the apparent residue function, where K_(a) is quantifying an apparent rate of contrast agent extravasation from plasma to extravascular, extracellular space (EES); determining an extravasation corrected residue function, R_(corr)(t), from the apparent residue function R_(ps)′(t) and the estimated K_(a), wherein the extravasation corrected residue function, R_(corr)(t), is determined using at least one of the following algorithms: R _(corr)(t)=R _(ps)′(t)−K _(a) R _(corr)(t)=1/F(R _(ps)′(t)−K _(a)(1−k _(ep) t)) R _(corr)(t)=1/F(R _(ps)′(t)−K _(α) e ^(−k) ^(ep) ^(t)) R _(corr)(t)=1/F(R _(ps)′(t)−mean[R _(ps)′(t>t _(tp))]); where F is the tissue flow and t_(tp) is an estimated start time of the tail part and where k_(ep) is a second leakage rate constant which is quantifying an apparent rate of contrast agent reflux from tissue back to blood.
 2. A method for estimating contrast agent extravasation in contrast agent based perfusion imaging methods to be performed by an electronic processor, the method comprising: accessing perfusion image data comprising a signal related to contrast agent concentration as a function of time in a voxel during the first and consecutive passages of the contrast agent through the vascular system; representing the signal by a convolution, R_(ps)′(t)

C_(p)′(t), of an apparent residue function, R_(ps)′(t), and an estimated contrast agent concentration in plasma, C_(p)′(t), and determining the apparent residue function R_(ps)′(t) by deconvolution of the signal with C_(p)′(t); estimating a first leakage rate constant K_(a) from a tail part of the apparent residue function, where K_(a) is quantifying an apparent rate of contrast agent extravasation from plasma to extravascular, extracellular space (EES), wherein the tail part of the apparent residue function is determined by one or more of: fitting a singly peaked, monotonously decreasing function, L(t), with zero asymptotes to a global maxima peak of the apparent residue function and defining the tail part of the apparent residue function as the part where the amplitude of the apparent residue function is consistently larger than the amplitude of L(t); estimating the approximate mean transit time (MTT) from the perfusion image data, and from this estimate, estimating a time, t_(fp), larger than MTT and using R′(t) for t>t_(fp) as the tail part of the apparent residue function; finding the section of the apparent residue function following its peak amplitude with minimum relative variance (variance divided by mean value) over a predefined section length.
 3. A method for estimating contrast agent extravasation in contrast agent based perfusion imaging methods to be performed by an electronic processor, the method comprising: accessing perfusion image data comprising a signal related to contrast agent concentration as a function of time in a voxel during the first and consecutive passages of the contrast agent through the vascular system; representing the signal by a convolution, R_(ps)′(t)

C_(p)′(t), of an apparent residue function, R_(ps)′(t), and an estimated contrast agent concentration in plasma, C_(p)′(t), and determining the apparent residue function R_(ps)′(t) by deconvolution of the signal with C_(p)′(t); estimating a first leakage rate constant K_(a) from a tail part of the apparent residue function, where K_(a) is quantifying an apparent rate of contrast agent extravasation from plasma to extravascular, extracellular space (EES); and wherein K_(a) is estimated as being proportional to a mean value of the tail part of the apparent residue function.
 4. A method for estimating contrast agent extravasation in contrast agent based perfusion imaging methods to be performed by an electronic processor, the method comprising: accessing perfusion image data comprising a signal related to contrast agent concentration as a function of time in a voxel during the first and consecutive passages of the contrast agent through the vascular system; representing the signal by a convolution, R_(ps)′(t)

C_(ps)′(t), of an apparent residue function, R_(ps)′(t), and an estimated contrast agent concentration in plasma, C_(p)′(t), and determining the apparent residue function R_(ps)′(t) by deconvolution of the signal with C_(p)′(t); estimating a first leakage rate constant K_(a) from a tail part of the apparent residue function, where K_(a) is quantifying an apparent rate of contrast agent extravasation from plasma to extravascular, extracellular space (EES); and wherein K_(a) is estimated as being proportional to an asymptote of the apparent residue function.
 5. A method according to claim 1, for estimating contrast agent extravasation in contrast agent based perfusion imaging methods to be performed by an electronic processor, the method comprising: accessing perfusion image data comprising a signal related to contrast agent concentration as a function of time in a voxel during the first and consecutive passages of the contrast agent through the vascular system; representing the signal by a convolution, R_(ps)′(t)

C_(p)′(t), of an apparent residue function, R_(ps)′(t), and an estimated contrast agent concentration in plasma, C_(p)′(t), and determining the apparent residue function R_(ps)′(t) by deconvolution of the signal with C_(p)′(t); estimating a first leakage rate constant K_(a) from a tail part of the apparent residue function, where K_(a) is quantifying an apparent rate of contrast agent extravasation from plasma to extravascular, extracellular space (EES); and wherein the estimation comprises fitting an exponential or linear function involving K_(a) as a constant to at least the tail part of the apparent residue function.
 6. A method for estimating contrast agent extravasation in contrast agent based perfusion imaging methods to be performed by an electronic processor, the method comprising: accessing perfusion image data comprising a signal related to contrast agent concentration as a function of time in a voxel during the first and consecutive passages of the contrast agent through the vascular system; representing the signal by a convolution, R_(ps)′(t)

C_(p)′(t), of an apparent residue function, R_(ps)′(t), and an estimated contrast agent concentration in plasma, C_(p)′(t), and determining the apparent residue function R_(ps)′(t) by deconvolution of the signal with C_(p)′(t); estimating a first leakage rate constant K_(a) from a tail part of the apparent residue function, where K_(a) is quantifying an apparent rate of contrast agent extravasation from plasma to extravascular, extracellular space (EES); and wherein the estimation further comprises estimating a second leakage rate constant k_(ep) quantifying an apparent rate of contrast agent reflux EES back to plasma based on the tail part of the apparent residue function.
 7. A method for estimating contrast agent extravasation in contrast agent based perfusion imaging methods to be performed by an electronic processor, the method comprising: accessing perfusion image data comprising a signal related to contrast agent concentration as a function of time in a voxel during the first and consecutive passages of the contrast agent through the vascular system; representing the signal by a convolution, R_(ps)′(t)

C_(p)′(t), of an apparent residue function, R_(ps)′(t), and an estimated contrast agent concentration in plasma, C_(p)′(t), and determining the apparent residue function R_(ps)′(t) by deconvolution of the signal with C_(p)′(t); estimating a first leakage rate constant K_(a) from a tail part of the apparent residue function, where K_(a) is quantifying an apparent rate of contrast agent extravasation from plasma to extravascular, extracellular space (EES); and an automated segmentation of imaged tissue into a tumor region and white and/or grey matter, and wherein a mean value of K_(a) are estimated for the tumor region and for the white and/or grey matter.
 8. A method for estimating contrast agent extravasation in contrast agent based perfusion imaging methods to be performed by an electronic processor, the method comprising: accessing perfusion image data comprising a signal related to contrast agent concentration as a function of time in a voxel during the first and consecutive passages of the contrast agent through the vascular system; representing the signal by a convolution, R′(t)

C_(p)′(t), of an apparent residue function, R_(ps)′(t), and an estimated contrast agent concentration in plasma, C_(p)′(t), and determining the apparent residue function R_(ps)′(t) by deconvolution of the signal with C_(p)′(t); estimating a first leakage rate constant K_(a) from a tail part of the apparent residue function, where K_(a) is quantifying an apparent rate of contrast agent extravasation from plasma to extravascular, extracellular space (EES); and wherein K_(a) is allowed to take both positive and negative values, and wherein the method further comprises separating between T₁- and T₂*-dominant leakage by determining the sign of K_(a), so that negative K_(a) values reflect T₁-dominant leakage effects and positive K_(a) values reflect T₂*-dominant leakage effects.
 9. A method for estimating contrast agent extravasation in contrast agent based perfusion imaging methods to be performed by an electronic processor, the method comprising: accessing perfusion image data comprising a signal related to contrast agent concentration as a function of time in a voxel during the first and consecutive passages of the contrast agent through the vascular system; representing the signal by a convolution, R_(ps)′(t)

C_(p)′(t), of an apparent residue function, R_(ps)′(t), and an estimated contrast agent concentration in plasma, C_(p)′(t), and determining the apparent residue function R_(ps)′(t) by deconvolution of the signal with C_(p)′(t); estimating a first leakage rate constant K_(a) from a tail part of the apparent residue function, where K_(a) is quantifying an apparent rate of contrast agent extravasation from plasma to extravascular, extracellular space (EES); and wherein the apparent residue function, R_(ps)′(t), is estimated as: ${{R_{ps}}^{\prime}(t)} = {{{R_{ps}(t)} + e} = {{F\begin{bmatrix} {R\left( t_{0} \right)} \\ {R\left( t_{1} \right)} \\ \vdots \\ {R\left( t_{N - 1} \right)} \end{bmatrix}} + {K_{a}\begin{bmatrix} {\mathbb{e}}^{{- k_{ep}}t_{0}} \\ {\mathbb{e}}^{{- k_{ep}}t_{1}} \\ \vdots \\ {\mathbb{e}}^{{- k_{ep}}t_{N - 1}} \end{bmatrix}}}}$ where e is an error term due to leakage, R(t) is a tissue specific residue function, F is proportional to tissue flow, N is a number of data-points, and k_(ep) is a rate constant from the EES to the intravascular space.
 10. A method for estimating contrast agent extravasation in contrast agent based perfusion imaging methods to be performed by an electronic processor, the method comprising: accessing perfusion image data comprising a signal related to contrast agent concentration as a function of time in a voxel during the first and consecutive passages of the contrast agent through the vascular system; representing the signal by a convolution, R_(ps)′(t)

C_(p)′(t), of an apparent residue function, R_(ps)′(t), and an estimated contrast agent concentration in plasma, C_(p)′(t), and determining the apparent residue function R_(ps)′(t) by deconvolution of the signal with C_(p)′(t); estimating a first leakage rate constant K_(a) from a tail part of the apparent residue function, where K_(a) is quantifying an apparent rate of contrast agent extravasation from plasma to extravascular, extracellular space (EES); and wherein the apparent residue function, R_(ps)′(t), is estimated as: ${{R_{ps}}^{\prime}(t)} = {{{R_{ps}(t)} + e} = {{F\begin{bmatrix} 1 \\ {R\left( t_{1} \right)} \\ \vdots \\ {R\left( t_{C} \right)} \\ 0 \\ 0 \\ \vdots \\ 0 \end{bmatrix}} + {K_{a}\begin{bmatrix} 0 \\ 0 \\ \vdots \\ 0 \\ 1 \\ {\exp\left( {{- K^{trans}}\Delta\;{t/v_{e}}} \right)} \\ \vdots \\ {\exp\left( {{- K^{trans}}N\;\Delta\;{t/v_{e}}} \right)} \end{bmatrix}}}}$ where e is an error term due to leakage, R(t) is a tissue specific residue function, F is proportional to tissue flow, Δt is a sampling interval, N is a number of data-points, t_(c) is a time index corresponding to a capillary transit time of the CA, T_(c), K^(trans) is a transfer constant describing the CA flux from the IVS to the EES, and ν_(e) is a leakage space per unit volume.
 11. A method for estimating contrast agent extravasation in contrast agent based perfusion imaging methods to be performed by an electronic processor, the method comprising: accessing perfusion image data comprising a signal related to contrast agent concentration as a function of time in a voxel during the first and consecutive passages of the contrast agent through the vascular system; representing the signal by a convolution, R_(ps)′(t)

C_(p)′(t), of an apparent residue function, R_(ps)′(t), and an estimated contrast agent concentration in plasma, C_(p)′(t), and determining the apparent residue function R_(ps)′(t) by deconvolution of the signal with C_(p)′(t); estimating a first leakage rate constant K_(a) from a tail part of the apparent residue function, where K_(a) is quantifying an apparent rate of contrast agent extravasation from plasma to extravascular, extracellular space (EES); and estimating a factor to be used in correction of partial volume (PV) effects in contrast agent based perfusion MR or CT images to be performed by an electronic processor, the method comprising determining a PV correction factor, f_(pv), as a ratio between parts of the signal following the first passage of the contrast agent from one or more voxels comprising arterial blood and one or more voxels filled with venous blood, respectively.
 12. A method of distinguishing between T₁-dominant and T₂*-dominant extravasation effects in perfusion imaging to be performed by an electronic processor, the method comprising: accessing perfusion image data comprising a signal related to contrast agent concentration as a function of time in a voxel during the first and consecutive passages of the contrast agent through the vascular system; representing the signal by a convolution, R_(ps)′(t)

C_(p)′(t), of an apparent residue function, R_(ps)′(t), and an estimated contrast agent concentration in plasma, C_(p)′(t), and determining the apparent residue function R_(ps)′(t) for each voxel by deconvolution of the signal with C_(p)′(t); determining a sign of the tail part of the apparent residue function; and generating an image of a parameter reflecting the determined sign and magnitude.
 13. An automated method for DSC-MRI comprising the following to be performed by an electronic processor for at least each slice in acquired image data: automatic detection of an arterial input function (AIF); estimating a first leakage rate constant K_(a) quantifying an apparent rate of contrast agent extravasation and a partial volume correction factor, f_(pv), according to claim
 7. 